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2 years ago

Re-write the quadratic function below in Standard Form y = -(x – 3)2 +8

Mathematics

1 answer:

lisov135 [29]2 years ago

4 0

Answer:

y = -x² + 6x - 1

General Formulas and Concepts:

Algebra I

Standard Form: ax² + bx + c = 0
Expanding by FOIL (First Inside Outside Last)
Combining like terms

Step-by-step explanation:

Step 1: Define equation

y = -(x - 3)² + 8

Step 2: Rewrite

Expand [FOIL]: y = -(x² - 6x + 9) + 8
Distribute -1: y = -x² + 6x - 9 + 8
Combine like terms: y = -x² + 6x - 1

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The port of South Louisiana, located along 54 miles of the Mississippi River between New Orleans and Baton Rouge, is the largest

Ksenya-84 [330]

Answer:

a) 0.7287

b) 0.9663

c) 0.237

d) 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 4.5 million tons of cargo per week

Standard Deviation, σ = 0 .82 million tons

We are given that the distribution of number of tons of cargo handled per week is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

a) P( port handles less than 5 million tons of cargo per week)

P(x < 5)

$P( x < 5) = P( z < \displaystyle\frac{5 - 4.5}{0.82}) = P(z < 0.609)$

Calculation the value from standard normal z table, we have,

$P(x < 5) =0.7287= 72.87\%$

b) P( port handles 3 or more million tons of cargo per week)

$P(x \geq 3) = P(z \geq \displaystyle\frac{3-4.5}{0.82}) = P(z \geq −1.82926)\\\\P( z \geq −1.82926) = 1 - P(z < -1.829)$

Calculating the value from the standard normal table we have,

$1 - 0.0337 = 0.9663 = 96.63\%\\P( x \geq 3) = 96.63\%$

c)P( port handles between 3 million and 4 million tons of cargo per week)

$P(3 \leq x \leq 4) = P(\displaystyle\frac{3 - 4.5}{0.82} \leq z \leq \displaystyle\frac{4-4.5}{0.82}) = P(-1.829 \leq z \leq -0.609)\\\\= P(z \leq -0.609) - P(z < -1.829)\\= 0.271-0.034 = 0.237= 23.7\%$

$P(3 \leq x \leq 4) = 23.7\%$

d) P(X=x) = 0.85

We have to find the value of x such that the probability is 0.85.

P(X > x)

$P( X > x) = P( z > \displaystyle\frac{x - 4.5}{0.82})=0.85$

$= 1 -P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.85$

$=P( z \leq \displaystyle\frac{x - 4.5}{0.82})=0.15$

Calculation the value from standard normal z table, we have,

$P( z \leq -1.036) = 0.15$

$\displaystyle\frac{x - 4.5}{0.82} = -1.036\\x = 3.65$

Thus, 3.65 tons of cargo per week or more that will require the port to extend its operating hours.

8 0

2 years ago

Express a decimal number ( ie 0.768) - process description please - as a rational number (96/125)?

Stels [109]

The decimal representation of any number is a linear combination of powers of 10. In other words, given a number like 123.456, we can expand it as

$1\cdot10^2+2\cdot10^1+3\cdot10^0+4\cdot10^{-1}+5\cdot10^{-2}+6\cdot10^{-3}$

$10^{-n}=\dfrac1{10^n}$ for any $n$ , so the above is the same as

$100+20+3+\dfrac4{10}+\dfrac5{100}+\dfrac6{1000}=\dfrac{100000+20000+3000+400+50+6}{1000}=\dfrac{123456}{1000}$

Similarly, we can write

$0.768=\dfrac{768}{1000}$

Now it's a question of reducing the fraction as much as possible. We have $\mathrm{gcd}(768,1000)=8$ so

$\dfrac{768}{1000}=\dfrac{96\cdot8}{125\cdot8}=\dfrac{96}{125}$

5 0

3 years ago

The sum of ten consecutive whole even numbers is 1190

olga2289 [7]

X + x+2 + x+4 + x+6 +x+8 + x+10 + x+12 + x+14 + x+16 + x+18 = 1190
Now simplify
10x + 90 = 1190
10x = 1100
x = 110
Now plug in 110 for x

5 0

3 years ago

Change this radical to an algebraic expression with fractional exponents. <img src="https://tex.z-dn.net/?f=%5Csqrt%7Bb%7D"

vovangra [49]

Answer:

is there options for the answer?

4 0

2 years ago

Question 4 Choose all numbers that make the inequality true. -1 >p

devlian [24]

Answer:

0 and above

Step-by-step explanation:

it can go onto infinity put 0 or Amy positive number and you got it

3 0

2 years ago